The use of Fourier transforms is a well known and established data processing technique enabling high resolution mass spectra to be obtained from mass spectrometers which acquire data in the form of a transient, for example by detection of an induced oscillating image current. The technique will be referred to herein as Fourier transform mass spectrometry (FTMS) and description of the technique can be found, for example, in Marshall, A. G. & Verdun, F. R., Fourier Transforms in NMR, Optical and Mass Spectrometry; A User's Handbook, Elsevier, 1990. Examples of such mass spectrometers include Fourier transform ion cyclotron resonance (FT-ICR) mass spectrometers and electrostatic orbital trapping mass spectrometers such as the Orbitrap™ mass spectrometer from Thermo Fisher Scientific. Such spectrometers offer superior performance in many respects, such as high sensitivity, mass accuracy, resolving power and dynamic range.
In the aforesaid types of mass spectrometer the ions being analysed are urged to undergo oscillatory motion within the spectrometer which induces a correspondingly oscillatory image charge in neighbouring detection electrodes which enables detection of the ions. The oscillatory motion may be of various forms including, for example, circular oscillatory motion in the case of FT-ICR and axial oscillatory motion whilst orbiting about a central electrode in the case of the Orbitrap™ mass spectrometer. The oscillatory image charge in turn induces an oscillatory image current in circuitry connected to the detection electrodes, which is then typically amplified, digitised and stored in computer memory as a transient (i.e. a signal in the time domain). The oscillating ions induce oscillatory image charge and oscillatory current at frequencies which are related to the mass-to-charge (m/z) values of the ions. Each ion of a given mass to charge (m/z) value will oscillate at a corresponding given frequency such that it contributes a signal to the transient which is generally in the form of a sine-shaped wave at the given frequency. The total detected image current of the transient is then the resultant sum of the image currents at all the frequencies present (i.e. a sum of sine waves signals). Fourier transformation of the transient yields the oscillation frequencies associated with the particular detected oscillating ions and from the frequencies the m/z values of the ions can be determined (i.e. the mass spectrum) by known equations.
Fourier transformation of the digitised transient is a fast processing method but requires relatively long detection times to achieve high resolving powers. While being adequate for most present-day Liquid Chromatography (LC) separations, the mass spectra acquisition rate for the highest resolving power needs to be increased to address ever faster separations methods. It is thus desirable to further increase the resolving power for a given acquisition time. However, there exist obstacles to the improvement of resolving power. Technical solutions like e.g. increase of the magnetic field in FT-ICR-MS or changes to the field geometry and voltages of an Orbitrap-MS may be difficult or prohibitively expensive.
The Fourier transformation of the transient provides a complex value for each point in the frequency domain (a complex spectrum), which is usually represented as a pair of two values: magnitude and phase or real (Re) and imaginary (Im) component. A special case is the representation of the complex spectrum as ‘absorption’ and ‘dispersion’ spectra. Here, in analogy to optical spectroscopy, the complex plane is turned such that the phase at the centre of the peak is zero. In this representation the first ‘absorption’ part gives a spectrum that maximizes at the centre of the peak and the second ‘disperison’ part gives a spectrum that has a zero-crossing at the centre of the peak.
Whilst the absorption spectrum can theoretically be used for forming the frequency and mass spectrum, as is the case in FT-NMR and FT-IR spectroscopy, in practice in the area of Fourier transform mass spectrometry, as described below, usually the so-called magnitude spectrum is displayed and used for data analysis, even though a magnitude spectrum has a significantly larger peak width than the absorption spectrum. For example a peak width for a Lorentzian peak shape is broadened by a factor of √3by the magnitude calculation.
Without perfect phase correction a lessening of peak position accuracy is caused by the phase variation with frequency of the various components constituting the transient which results, e.g., from the typical time delays inherent between excitation and/or injection of ions into the mass analyser and the start of detection of the transient. This phase variation problem produces asymmetrical peak shapes for the real component following the Fourier transformation. A totally symmetrical peak is only obtained when the phase angle at the start of the transient is zero. In order to restore symmetry to the peaks in the frequency and hence mass domains, FTMS data systems have conventionally used the so-called magnitude spectrum given by:Magnitude(p)=[Re(p)2+Im(p)2]1/2  Equation (1)
where Magnitude(p) is the magnitude value at a point p; Re(p) is the real component from the Fourier transformation at point p; and Im(p) is the imaginary component from the Fourier transformation at point p. The point p is typically a point in the frequency (f) domain or a domain related thereto such as the m/z domain. The m/z value can be derived from the frequency of the magnitude peak's centre. The use of the magnitude spectrum, which amounts to disregarding the phase information, yields symmetrical peaks in the frequency/mass spectra but suffers from reduced resolving power compared to the pure absorption spectrum.
Sometimes, especially when computational expense is an issue, the power spectrum (Power(p)=[Re(p)2+Im(p)2]) or an approximation to the magnitude spectrum is used instead of the magnitude spectrum. A frequently used and considerably accurate approximation to [Re(p)2+Im(p)2]1/2 is, for example, to use                (a) Estimate=0.96|Re(p)|+0.398|Im(p)|for |Re(p)|>|Im(p)|, and        
(b) Estimate=0.96|Im(p)|+0.398|Re(p)| otherwise
where |Re(p)| and |Im(p)| are respectively the absolute value of the real (or imaginary) component. This is especially convenient after an initial phase correction has been done, because then the relation of Re and Im to each other are known and (a) or (b) can be applied without first having to test for whether |(Re(p)|>|Im(p)|.
For convenience herein it will refer to a spectrum from the class of the thus generated spectra (e.g. any of Power spectrum, Magnitude spectrum, estimates to the Magnitude spectrum or Power spectrum, or other combinations of real and imaginary parts of the Fourier transform that give a similar effect to the Magnitude spectrum or Power spectrum), i.e. a spectrum which comprises a function of real and imaginary components of the complex spectrum where substantially all points have the same sign, as a “Positive Spectrum”.
Various approaches to tackling the phase problem therefore have been proposed in the prior art, including phase correction, the aim of which has been to try to ensure that each of the frequency components exhibits a peak shape close to a pure absorption peak shape.
In U.S. Pat. No. 7,078,684, an FT-ICR system is described in which hardware is designed to minimise the delay between ion excitation and detection by synchronising these steps so as to be simultaneous and software deconvolutes the Fourier transformed frequency domain data using complex division to obtain a separate absorption spectrum. This enables use of the symmetrical absorption spectrum for obtaining the mass spectrum and is reported to improve the resolving power by a factor of 2 compared to the use of the magnitude spectrum. However, the approach described in U.S. Pat. No. 7,078,684 is not useful in the case of electrostatic orbital trapping mass spectrometers like the Orbitrap™ mass analyser operated without excitation but instead with excitation-by-injection, since current ion injection methods for injecting ions into the mass analyser involve changing the trapping field during injection so that the oscillation frequencies of the ions during this initial injection period are also changing. In the case of the Orbitrap™ mass analyser therefore, the time delay between ion injection and detection is difficult to minimise. Additionally the method of U.S. Pat. No. 7,078,684 proves, regardless of analyser type, to suffer from sidelobe problems (discussed further below) and mass accuracy problems relating to the limited quality of phase correction.
In the prior art such as B. A. Vining, R. E. Bossio and A. G. Marshall, Anal. Chem., 1999, 71 (2), pp 460-467 algorithms for phase correction of ion oscillations in the acquired spectra have enabled the absorption spectrum to be used for conversion into mass spectra instead of magnitude spectra and as a consequence has improved the resolving power by a factor of 2 compared to the use of the magnitude spectrum.
However, a problem of simply applying a phase correction to the data is that transformed peaks in the resultant frequency or mass spectra suffer from a problem of spectral artefacts such as large sidelobes beside peaks and a baseline curve or roll can be introduced. Sidelobes can be a particular problem if a second or further peak is in the position of one of the sidelobes and so becomes disturbed or even lost from the spectrum. These problems are inherent in the methods described above and the solution in those methods is to hide the appearance of sidelobes in the spectrum by use of “half-Hanning” apodisation and accept a high degree of spectral leakage, leading to distortion of neighbouring peaks over a broader region and an overall increase in “noise”. In addition, the sidelobe problem is not really solved but just hidden under the spectral leakage of other peaks. The displayed data may also be subject to baseline clipping which improves the appearance of the spectra but also leads to errors. Another negative impact of a simple linear phase correction is to reduce mass accuracy due to mass dependent phase variations which is not addressed by those methods.
In the wider art of Fourier transforms applying some form of window (“windowing”), also known as apodisation, to the pre-transformed time domain data is known as a means to reduce the appearance of sidelobes in the transform data, e.g. Hamming, Hanning (Hann) or half-Hanning (half-Hann) apodisation. Description of such techniques can be found, e.g., in Lee, J. P. & Comisarow, M. B., Advantageous Apodization Functions for Magnitude-Mode Fourier Transform Spectroscopy, Applied Spectroscopy, 1987, 41, 93-98.
A problem with windowing or apodisation, however, is that the transformed peak becomes broadened, i.e. the resolving power is lessened. There have also been described various approaches to the reducing of peak sidelobes in Fourier transformations such as those methods disclosed in U.S. Pat. No. 5,349,359 and U.S. Pat. No. 5,686,922 which are methods of sidelobe reduction for use in radar systems and are not primarily disclosed for use in mass spectrometry. The methods of those references do not use the pure “absorption” spectrum but use the magnitude spectrum, combining apodised and unapodised data to construct a peak that is not broadened by apodization and has no or reduced sidelobes.
It therefore remains a problem to be able to more effectively and efficiently achieve increased resolving power, e.g. as provided by a pure absorption spectrum, especially to be able to produce cleaner peaks with reduced or removed significant sidelobes and a lower extent of spectral leakage, together with higher resolving power.
In view of the above background, the present invention has been made.